What is the integral from-1 to-2 of ((16-x^3)/(x^3)) ?

The integral from-1 to-2 of ((16-x^3)/(x^3)) is 7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to-2 of ((16-x^3)/(x^3))

\int_{- 1}^{- 2} (\frac{16 - x ^{3}}{x ^{3}}) d x

7

Solution steps

\int_{- 1}^{- 2} \frac{16 - x ^{3}}{x ^{3}} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{- 1} \frac{16 - x ^{3}}{x ^{3}} d x

Expand

\frac{16 - x ^{3}}{x ^{3}} : \frac{16}{x ^{3}} - 1

= - \int_{- 2}^{- 1} \frac{16}{x ^{3}} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (\int_{- 2}^{- 1} \frac{16}{x ^{3}} d x - \int_{- 2}^{- 1} 1 d x)

\int_{- 2}^{- 1} \frac{16}{x ^{3}} d x = - 6

\int_{- 2}^{- 1} 1 d x = 1

= - (- 6 - 1)

Simplify

= 7

f (x) = x - 7

\frac{d}{d x} (\frac{x + x ^{3}}{x ^{2}})

x 18 - x^{2}

t e^{3 t}

f (x) = \frac{1}{x - 8}, (- 1, - \frac{1}{9})

What is the integral from-1 to-2 of ((16-x^3)/(x^3)) ?
The integral from-1 to-2 of ((16-x^3)/(x^3)) is 7